Novice Solution (Level 2)
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Here are seven basic steps you can learn to solve the rubik's cube. This method differs from the easy method in the last layer, so if you've already learned the easy method, skip ahead to step 4. Keep in mind that it is possible to "get lucky" and skip any of the seven steps (if they are already done). There are other methods that are much quicker than this, but they require more memorization. If you would like to learn to solve the rubik's cube quickly, look at the more advanced methods.
Step 1
Form a cross on one of the faces, like this:

Whatever color you choose for the cross will be your bottom color. I recommend using white, because the edge pieces you'll need will be easier to spot on the cube. First, find an edge piece with your bottom color, and put it so that both of its sides match up with their respective centers, like this:

Doing it three more times will yield this (notice the cross on the bottom):

If the cube looks like this, it is wrong:

You are now done with the cross.


Step 2
Finish the bottom by solving the four corners that have your bottom color on them. Check if the corner is oriented this way:

You should solve this case with U' F' U F. Do not memorize this. Understand it. The first move gets the corner out of the way, so you can do the second move without disturbing it. The third move connects the corner correctly to the edge piece it goes next to, and the final move puts everything back into place. The corner can be situated in other ways, also. Use the following moves to solve them (You should be able to figure them out on your own).
U R U' R'
Do something like R U' R' or F' U F to turn this case into one of the first two.
or do something like R U' R' or R U R' or F' U F or F' U' F to turn this case into one of the first three cases.
There are other possibilities for the location of the corner- these cases are only when the corner is above the place it needs to go. You should be able to apply what you have learned to figure them out on your own. You are now done with the bottom layer corners.


Step 3
You should now have one solid face, your bottom face, with a solid band running around it. Try not to think of it this way, think of it as having finished the bottom layer of the cube. You must now do the middle layer, but there are only four pieces in it, since centers don't move (with respect to each other) and don't count. Find an edge piece in the top layer that needs to go into the middle layer (It is possible, but unlikely, that there are none in the top layer. I will explain what to do in this situation later). An easy way of finding one is looking for an edge piece in the top layer that doesn't have the top layer color. Spin the U face until the edge is lined up with one of its centers. This means spin the U face until your edge is one of the two pictures below, and do the moves next to the corresponding picture.
U R U' R' U' F' U F
U' F' U F U R U' R'
If there are no edges that you need in the top layer, then find an edge you need that is in the middle layer. It might be in the wrong place, or in the right place but flipped incorrectly. Use one of the two sets of moves above to displace the piece you need, or, in other words, place a wrong edge in the middle layer. When you do this it moves the edge you need into the top layer, so you can put it in the right spot. You are now done with the first two layers, and only one remains.


Step 4
The goal of this step is to create a cross on the top face (orient the edges). It will be different than the cross we made on the bottom, in that it doesn't have to match up to the faces on the sides. In other words, it would be fine if, when done this step, your cube looked like this:
Now, look at the top face, and identify which of the following cases you have, then perform the sequence of moves that is next to it.
F U R U' R' F'
F R U R' U' F'
F R B U2 B' U R' F' L' U2 L
When you are done this step, your cube should look like this:


Step 5
Now, make the cross line up on the sides (permute it), like you did with the bottom cross. By turning the U face, you will have one of the following cases. Do the appropriate sequence.
R B' R' B F R' F B' R' B R F2
L U L' U L U2 L'
R' U' R U' R' U2 R
Now, the only thing wrong with your cube is the top four corners (1 or more of which might already be correct).


Step 6
Now you should not turn the U face anymore, unless it is part of a sequence, because you will mess up the edges, but you can, and will, rotate the entire cube occasionally (looking at it from a different side) in order to make your cube look like one of the cases. You will now place the corners. It doesn't matter if they are twisted correctly. Use the sequences below.
U R2 F2 B2 L2 D R2 F2 B2 L2
R' L D' L' D R U2 R' D' L D R L'
L U' R' U L' U' R U
R' U L U' R U L' U'
The only thing left to do is to twist the corners correctly.


Step 7
This step is more confusing than most. You will solve the corners in pairs. You will solve one corner, and the cube will seem messed up, but don't panic! You will then solve another corner, simultaneously restoring the cube.

Two corners are wrong
Put one corner in the top-front-right position. To rotate it clockwise, do F D2 F' R' D2 R. To rotate it counter-clockwise, do R' D2 R F D2 F'. Then move U until the other corner is in the top-front-right position. MOVE U TO DO THIS, NOT THE WHOLE CUBE! This corner will need to go the opposite direction that the first corner needed to go. Do the appropriate sequence. Then just move U again to solve the cube.

Four corners are wrong
Do what you would do for two corners, but after you have solved the first corner and looking for another one, don't put just any corner in the top-front-right position, find one that needs to go the opposite direction that the first one did. Now there will only be two corners left.

Three corners are wrong
The three corners will all need to go the same way, but two counter-clockwise turns are equivalent to one clockwise turn. Do what you would do for two corners: after the first corner is done, put any other corner in the top-front-right position, and turn it the opposite way that you turned the first one, EVEN THOUGH THIS WILL NOT SOLVE IT. Now you only have two corners left.